1. Electric Flux
how many lines?

2. Electric Flux
Through a closed surface

3. Electric Flux FE
Conceptually, the number of electric field lines passing through a surface E
FE = EA
A = area of the surface

4. Electric Flux FE
Previous formula only works when field is normal to the surface E
FE = 0

5. Electric Flux FE E q Area in profile is A cos q
q = angle of E field from surface normal
FE = EA cos q

6. Gauss’s Law
Flux through an enclosing surface is proportional to charge enclosed
FE = q/e0
e0 = “vacuum permittivity” = 8.85×10–12 C2/(Nm2)

7. Gauss’s law
Use flux to find field around a point charge

8. Field of a Point Charge What is area A of spherical shell?
FE = Qin/e0 = EA
Find E

9. Field around a Point Charge
Shell Area = 4pr2
FE = q/e0 = EA +q q
e0A q
e04pr2 R
E = = q
4pe0 r2 = kq r2 =
if k = 1
4pe0

10. Gauss’s Law Example Infinite plate of uniform charge density (Q/A) = s
Area of surface = 2A
Qin = As
FE = Qin/e0 = As/e0
FE = E(2A)
As/e0 = E(2A)
E = ½ s/e0 Q